Reanalysis of the Higgs boson decay <i>H</i> → <i>gg</i> up to ${\alpha }_{s}^{6}$-order level using the principle of maximum conformality

Zeng, Jun; Wu, Xing-Gang; Bu, Shi; Shen, Jian-Ming; Wang, Sheng-Quan

doi:10.1088/1361-6471/aace6f

Cited by 13 publications

(23 citation statements)

References 45 publications

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“…where the error is the residual scale dependence, which mainly comes from the NLO-terms. As a comparison, it has been found that the renormalization scale uncertainty for N 4 LO using the conventional scale setting is +2.1 −1.3 KeV [145], which is larger than that of PMC prediction but is also small. This indicates that if one knows enough higher-order terms, the conventional scale uncertainty can also be suppressed to a certain degree.…”

Section: The Residual Renormalization Scale Dependencementioning

confidence: 95%

“…In some cases, a weak perturbative convergence may be exist in a PMC scale; the residual scale dependence for this particular scale may be large, leading to a comparatively larger residual scale dependence for the pQCD approximant. As an example, it has been found that there is comparatively large µ r dependence for the NLO PMC scale Q 2 for H → gg process, leading to a larger residual scale dependence for H → gg decay width [128,145]. Figure 7 shows that the precision of Q 2 increases as more loop terms have been taken into consideration.…”

Section: The Residual Renormalization Scale Dependencementioning

confidence: 99%

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The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality

Shen

et al. 2019

Progress in Particle and Nuclear Physics

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The conventional scale setting approach to fixed-order perturbative QCD (pQCD) predictions is based on a guessed renormalization scale, usually taking as the one to eliminate the large logterms of the pQCD series, together with an arbitrary range to estimate its uncertainty. This ad hoc assignment of the renormalization scale causes the coefficients of the QCD running coupling at each perturbative order to be strongly dependent on the choices of both the renormalization scale and the renormalization scheme, which leads to conventional renormalization scheme-andscale ambiguities. However, such ambiguities are not necessary, since as a basic requirement of renormalization group invariance (RGI), any physical observable must be independent of the choices of both the renormalization scheme and the renormalization scale. In fact, if one uses the Principle of Maximum Conformality (PMC) to fix the renormalization scale, the coefficients of the pQCD series match the series of conformal theory, and they are thus scheme independent. The PMC predictions also eliminate the divergent renormalon contributions, leading to a better convergence property. It has been found that the elimination of the scale and scheme ambiguities at all orders relies heavily on how precisely we know the analytic form of the QCD running coupling α s . In this review, we summarize the known properties of the QCD running coupling and its recent progresses, especially for its behavior within the asymptotic region. Conventional schemes for defining the QCD running coupling suffer from a complex and scheme-dependent renormalization group equation (RGE), or the β-function, which is usually solved perturbatively at high orders due to the entanglement of the scheme-running and scale-running behaviors. These complications * lead to residual scheme dependence even after applying the PMC, which however can be avoided by using a C-scheme couplingα s , whose scheme-and-scale running behaviors are governed by the same scheme-independent RGE. As a result, an analytic solution for the running coupling can be achieved at any fixed order. Using the C-scheme coupling, a demonstration that the PMC prediction is scheme-independent to all-orders for any renormalization schemes can be achieved. Given a measurement which sets the magnitude of the QCD running coupling at a specific scale such as M Z , the resulting pQCD predictions, after applying the single-scale PMC, become completely independent of the choice of the renormalization scheme and the initial renormalization scale at any fixed-order, thus satisfying all of the conditions of RGI. An improved pQCD convergence provides an opportunity of using the resummation procedures such as the Padé approximation (PA) approach to predict higher-order terms and thus to increase the precision, reliability and predictive power of pQCD theory. In this review, we also summarize the current progress on the PMC and some of its typical applications, showing to what degree the conventional renormalization scheme-and-scale ambiguities ...

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Section: The Residual Renormalization Scale Dependencementioning

confidence: 95%

Section: The Residual Renormalization Scale Dependencementioning

confidence: 99%

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality

Shen

et al. 2019

Progress in Particle and Nuclear Physics

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“…This dependence is expected to be suppressed when one includes higher loop terms. An example can be found for Higgs-boson decay H → gg[38].…”

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confidence: 99%

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

Sang

Huang

et al. 2021

J. High Energ. Phys.

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In the paper, we present QCD predictions for γ + ηc production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e+ + e− → γ + ηc using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the e+e− center-of-mass collision energy $$ \sqrt{s} $$ s . The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal β contributions into the QCD coupling αs(Q2). The renormalization group equation then sets the value of αs for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a renormalization scale-and-scheme independent prediction, σ|NNLO,PMC ≃ 41.18 fb for $$ \sqrt{s} $$ s =10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large K factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the Padé approximation approach, we predict σ|NNNLO,PMC+Pade ≃ 18.99 fb, which is consistent with the recent BELLE measurement $$ {\sigma}^{\mathrm{obs}}={16.58}_{-9.93}^{+10.51} $$ σ obs = 16.58 − 9.93 + 10.51 fb at $$ \sqrt{s} $$ s ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

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“…the logarithm L = ln Before applying the PMC to the R-ratio, we first transform the MS-scheme pQCD series (3) into the one under the minimal momentum space subtraction scheme (mMOM) [29,30]. This transformation avoids the confusion of distributing the n f -terms involving the three-gluon or fourgluon vertexes into the β-terms [31][32][33][34]. This transformation can be achieved by using the relation of the running coupling under the mMOM-scheme and the MS-scheme, e.g.…”

Section: Calculation Technologymentioning

confidence: 99%

The heavy quarkonium inclusive decays using the principle of maximum conformality

Zeng

Huang

et al. 2020

Eur. Phys. J. C

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The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $$\eta _Q$$ηQ (Q being c or b) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about $$\left( ^{+4\%}_{-34\%}\right) $$-34%+4% for $$\eta _c$$ηc and $$\left( ^{+0.0}_{-9\%}\right) $$-9%+0.0 for $$\eta _b$$ηb, by varying the scale within the range of $$[m_Q, 4m_Q]$$[mQ,4mQ]. The principle of maximum conformality (PMC) provides a systematic way to fix the $$\alpha _s$$αs-running behavior of the process, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the $$\eta _Q$$ηQ inclusive decay width can be greatly improved. Taking the relativistic correction $${\mathcal {O}}(\alpha _{s}v^2)$$O(αsv2) into consideration, the ratios of the $$\eta _{Q}$$ηQ decays to light hadrons or $$\gamma \gamma $$γγ are: $$R^\mathrm{NNLO}_{\eta _c}|_{\mathrm{PMC}}=(3.93^{+0.26}_{-0.24})\times 10^3$$RηcNNLO|PMC=(3.93-0.24+0.26)×103 and $$R^\mathrm{NNLO}_{\eta _b}|_{\mathrm{PMC}}=(22.85^{+0.90}_{-0.87})\times 10^3$$RηbNNLO|PMC=(22.85-0.87+0.90)×103, respectively. Here the errors are for $$\Delta \alpha _s(M_Z) = \pm 0.0011$$Δαs(MZ)=±0.0011. As a step forward, by applying the Pad$$\acute{e}$$e´ approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. $$R^{\mathrm{NNNLO}}_{\eta _c}|_{\mathrm{PAA+PMC}} =(5.66^{+0.65}_{-0.55})\times 10^3$$RηcNNNLO|PAA+PMC=(5.66-0.55+0.65)×103 and $$R^{\mathrm{NNNLO}}_{\eta _b}|_{\mathrm{PAA+PMC}}=(26.02^{+1.24}_{-1.17})\times 10^3$$RηbNNNLO|PAA+PMC=(26.02-1.17+1.24)×103. The $$R^{\mathrm{NNNLO}}_{\eta _c}|_{\mathrm{PAA+PMC}}$$RηcNNNLO|PAA+PMC ratio agrees with the latest PDG value $$R_{\eta _c}^\mathrm{{exp}}=(5.3_{-1.4}^{+2.4})\times 10^3$$Rηcexp=(5.3-1.4+2.4)×103, indicating the necessity of a strict calculation of NNNLO terms.

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Reanalysis of the Higgs boson decay H → gg up to ${\alpha }_{s}^{6}$-order level using the principle of maximum conformality

Cited by 13 publications

References 45 publications

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality

The QCD renormalization group equation and the elimination of fixed-order scheme-and-scale ambiguities using the principle of maximum conformality

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

The heavy quarkonium inclusive decays using the principle of maximum conformality

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